True displacement in EEVEE?
It seems that EEVEE doesn't support true displacement in the nodes and we don't know when it will. However, it is not so difficult to find another solution.

To replace animating math and displacement nodes, I used several Displace modifiers with different textures and empty objects which have keyframes on their LocRotScale. This approach is explained in detail here. I'd like also to highlight that in my case the Direction value was very important – displacement looked ugly before I limited it to Z axis only.